At a town hall meeting in Spartanburg, upstate South Carolina, Rick Santorum is in full flow.

"My children, when they'd read articles about me in the paper, they used to think my first name was 'Ultra'," he tells the crowd of 100 or so people scattered around the half-full function room.

"When you stick your head out of the fox hole on the issue of life, the issue of family, [the media] come after you, and they paint you as this far right person, who's so extreme that you believe marriage should be between a man and a woman.

"So extreme that you believe life begins at conception. I actually don't believe life begins at conception. I know life begins at conception."

The former Pennsylvania senator has built his campaign around what he calls "the fundamentals – faith, family and freedom". He takes pride in his willingness to address social issues, including gay marriage, abortion and stem cell research, criticising his rivals for their less strident approaches.

This strategy led him to an unexpected victory in the Iowa caucuses. But then, he came a disappointing third in conservative South Carolina. Now, he is barely campaigning in Florida; after Thursday's CNN debate in Jacksonville he will spend Friday and Saturday in Virginia.

But Santorum's core base of supporters are loyal and passionate. And the race has been volatile before: Gingrich appears on the slide in Florida – Santorum still believes he will pick up the "true conservative" vote. So who are the people who believe in the Santorum cause? And what is it about him that attracts them?

The morning after the Spartanburg event, the Santorum campaign headed 200 miles south, for an appearance in the more moderate Mount Pleasant, just across the bay from the college town of Charleston. Santorum largely stuck to his "fundamentals" as he spoke at the Memorial Waterfront Park, shielded from the brilliant sunlight by the looming Arthur Ravenel Jr bridge.

Listening amid the crowd of 50 or so enthusiasts was retired teacher Kathy Hughes, who said Santorum's position on social issues were a big part of why he had her vote.

"His integrity. He is a moral person and he has strong family values, and that's very important to me."

At campaign stops around South Carolina, from the more conservative north-west to the supposedly more moderate lowlands, supporters cite "family values" strikingly often as a reason for supporting him. It's an innocuous phrase, often used as a euphemism for less palatable messages on abortion and gays.

"I am pro-life because it's guaranteed to us by our creator and by our constitution that we will preserve life, and I do not agree that it's not important.

"I think it is an important issue and its been an important issue in American politics. It's important that we value the life of the unborn, or else we probably don't value the lives of anyone."

The next day, Friday, Santorum was appearing at the venerated Cidatel Military College in Charleston, at a Republican society dinner. He enjoyed huge support from cadets at the college, with several spending time at his campaign headquarters, phoning potential supporters.

Alex Angerman, a 20-year-old junior at the college, had consistently topped he "leadership chart" at the office for the most calls placed on behalf of Santorum per day.

"I love all his views on pro-life, and strong national defence, and his views on immigration," Angerman said. "I love his strong family values plan, and how he is a great man of God."

Angerman became aware of Santorum when the latter was a Pennsylvania senator – Angerman grew up in neighbouring New Jersey – and he became a firm supporter after a meeting at a Citadel Republican society meeting.

Angerman said any of the candidates could beat Obama, but he was drawn to Santorum: "He's much more of a conservative in my eyes than Romney."

"It seems that governor Romney has switched on some issues that I don't agree with, such as abortion and whatnot."

The Citadel event showed how Santorum can tailor his message while maintaining his core fundamentals of faith and family. Speaking to the pro-military crowd the former senator was cheered – Angerman was among those impressed – when he pledged to intervene in Iran, the first time he discussed intervention in three days of campaigning.

"I say to the people of Iran: 'We will help you get rid of these tyrants who are oppressing you and destroying your country'," Santorum said, arguing that there was a "moral case" to aid the Iranian people.

In upstate South Carolina, a manufacturing area home to a BMW plant which employs 7,000 workers, Santorum had similarly shown himself to be adaptable, as the pro-jobs candidate of the hard-working South Carolinian. Once again, his fundamentals were to the fore – billed as essential to the creation of jobs.

If people can achieve three things, the Pennsylvanian said – "work, graduate from high school, and get married before you have children" – then "the likelihood you will ever be in poverty in your lifetime is 2%".

"The likelihood you will earn above the median income at sometime in your lifetime is 77%. If you fail to do just one of those three things, not all of them, just one, the likelihood you will be in poverty is 74%.

"Now why can't we talk about the importance of work, the importance of family and marriage as key instituions of our society? Why can't we have a presidential candidate who says we need to have a society that nurtures the family, that supports the family."

It is a message which appears to have a lot of traction. Hovering at the entrance to Santorum's South Carolina headquarters – a rather stark, open plan office in Mount Pleasant – on Friday was Margaret Conway-Vogel, who had driven nine hours from Atlanta, Georgia, to volunteer.

What was so compelling about Santorum?

"Family values. Small government. Conservative perspectives," Conway-Vogel said without pause.

By family values, Conway-Vogel said, she meant "commitment to the values that this nation was founded on."

"I relocated from New York to Georgia. Not because I didn't love New York, but because it became so liberal and so anti-religion that I sought out a state that is more conservative and more open to family values, and small government, and responsible spending."

After the Citadel event, as the lights went up and the former senator went out, Caroline Mazzone, a fashion consultant who moved to South Carolina two years ago, was among those rating Santorum's performance, reaching for that familiar buzz word like so many fellow supporters.

"I love Rick Santorum because I think his family values are wonderful. I think his family's wonderful. I think he's everything that this United States needs in a president."

Asked why family values were important, Mazzone, 52, illustrated the devout support Santorum enjoys from Christians. Mazzone said she was brought up in a strict Catholic family and could relate to Santorum: "I think if he has strong family values, he can portray that to people in the rest of the United States."

"I think he is a devout Catholic, I think that he believes in going to church, I think he believes in following all the rules and regulations."

Chatting with Mazzone was Hayley Thrift, a PR consultant who grew up in Seneca, close to Greenville and Spartanburg in northern South Carolina, where Santorum had spoken about putting his head out of the foxhole two days earlier.

Thrift had been campaigning for Santorum in the state, and like Mazzone, found his faith a big selling point – describing him as "rock solid in his faith".

"He is truly a man that follows God. He encourages his family to do the same, and you talk to his children, and you talk to his wife and you can tell they all support each other, they all love each other.

"That's what America needs – to get back to core family values and to appreciate the family. Because so many children are growing up in broken homes and they don't know their parents and their parents are splitting up and it's very sad because I'm fortunate enough to have a strong family just like the Santorums, and I think that's what America needs."

Whether the rest of America agrees with Thrift – and with Santorum's fundamentals of faith, family and freedom – is a different matter.

Newt Gingrich, on his third marriage, is hardly the embodiment of traditional family values. A Catholic who was formerly a Baptist and a Lutheran, he is perhaps not the bedrock of faith that Santorum represents. Yet the former speaker managed to secure more support from the same bloc of voters that Santorum would have hoped to win.

It might be that Santorum's fundamentals are just not the right kind of fundamentals that America is looking for.